We have performed electron tunneling spectroscopy measurements on gated single and bilayer graphene devices with thin hexagonal boron nitride (h-BN) as a tunneling barrier. We can directly probe electronic structures of graphene devices by varying charge density, tunneling bias voltage and external magnetic fields. In addition, we can identify several spectra features which are in good agreement with the vibrational excitations; phonons of graphene and h-BN, and a signature of local plasmonic excitation. Upon increasing external magnetic field, the development of Landau levels (LL) is observed as early as 0.2 T and we are able to discern individual LL as many as 20 as an index for both filled and empty states, which is unprecedented in previous tunneling.